Some mathematical and numerical models in ecology, medicine, and epidemiology

For the ecological part, the presentation will focus on two recent topics of interest: the containment of invasive species and long-range interference.

In the first case, methods to halt or slow down invasion by making the environment hostile to the invader are studied.

For the second case, a relatively high-order numerical method is examined, determining its convergence analysis.

In the second part, a model to counter Alzheimer's is discussed. It is formulated to explore the effects of hypothetical treatments in silico. This should suggest to the industry where to focus efforts on developing new drugs to effectively slow down the disease. Finally, a multi-strain epidemiological model for the dynamics between vector and host in the spread of dengue is examined.